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Differential Geometry

From Elastic Curves to Willmore Surfaces
BuchKartoniert, Paperback
203 Seiten
Englisch
Springererschienen am14.02.20242024
This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.mehr

Produkt

KlappentextThis open access book covers the main topics for a course on the differential geometry of curves and surfaces. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.
Details
ISBN/GTIN978-3-031-39837-7
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2024
Erscheinungsdatum14.02.2024
Auflage2024
ReiheCompact Textbooks in Mathematics
Seiten203 Seiten
SpracheEnglisch
IllustrationenXI, 203 p. 80 illus., 66 illus. in color.
Artikel-Nr.54120986

Inhalt/Kritik

Inhaltsverzeichnis
- Part I Curves. - 1. Curves in Rn. - 2. Variations of Curves. - 3. Curves in R2. - 4. Parallel Normal Fields. - 5. Curves in R3. - Part II Surfaces. - 6. Surfaces and Riemannian Geometry. - 7. Integration and Stokes´ Theorem. - 8. Curvature. - 9. Levi-Civita Connection. - 10. Total Gaussian Curvature. - 11. Closed Surfaces. - 12. Variations of Surfaces . - 13. Willmore Surfaces.mehr

Autor

Ulrich Pinkall was born in 1955. In 1979 he graduated in Mathematics and Physics at the University of Freiburg, where in 1981 he also got his PhD in Mathematics. From 1984 to 1986 he worked at the MPI für Mathematik in Bonn. From 1986 to 2023 he taught Mathematics at the Technical University of Berlin. From 1995 to 1996 he was Five College Professor in Amherst. From 1992 to 2002 he was head of the Sonderforschungsbereich Differential Geometry and Quantum Physics.

Oliver Gross received his B.Sc. and M.Sc. in Mathematics at TU Berlin in 2019 and 2020 respectively. Currently he is a researcher in the collaborative research center SFB TRR 109 "Discretization in Geometry and Dynamics" at TU Berlin under the supervision of Prof. Ulrich Pinkall.